The numerical semigroup generated by relatively prime positive integers a1, . . . , an is the set S of all linear combinations of a1, . . . , an with nonnegative integral coefficients. The largest integer which is not an element of S is called the Frobenius number of S. Recently, J. M. Maŕın, J. L. Ramı́rez Alfonśın, and M. P. Revuelta determined the Frobenius number of a Fibonacci semigroup, th...

In this study, we present the notion of quasi-ordinarization transform a numerical semigroup. The set all semigroups fixed genus can be organized in forest whose roots are quasi-ordinary same genus. This way, approach conjecture on increasingness cardinalities sets each given We analyze number nodes at depth and propose new conjectures. Some properties presented, as well some relations between ...

— In this work we study some objects describing the addition behavior of a numerical semigroup and we prove that they uniquely determine the numerical semigroup. We then study the case of Arf numerical semigroups and find some specific results. Résumé (Comportement de l’addition dans un semi-groupe numérique). — Dans ce travail, nous étudions des objets qui décrivent le comportement de l’additi...

A proportionally modular numerical semigroup is the set of nonnegative integer solutions to a Diophantine inequality of the type axmod b ≤ cx . We give a new presentation for these semigroups and we relate them with a type of affine full semigroups. Next, we describe explicitly the minimal generating system for the affine full semigroups we are considering. As a consequence, we obtain generatin...